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用动力系统分岔方法研究了一类非线性色散Boussinesq方程.在不同的参数条件下,给出了该方程具有隐函数形式的孤立波解的解析表达式.数值模拟进一步验证了所得结果的正确性.
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关键词:
- 非线性色散Boussinesq方程 /
- 分岔方法 /
- 同宿轨道 /
- 隐式孤立波解
[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nolinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Wu Y Q 2010 Acta Phys. Sin. 59 1403 (in Chinese)[吴勇旗 2010 物理学报 59 1403]
[3] Huang W H 2009 Chin. Phys. B 18 3163
[4] Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 1476 (in Chinese)[曾 昕、 张鸿庆 2005 物理学报 54 1476]
[5] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 物理学报 47 353]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、 杨红娟 2010 物理学报 59 67]
[7] Li J B, Zhan Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
[8] Guo B L, Liu Z R 2005 Chaos Solitons Fract. 23 1451
[9] Shen J W, Xu W, Lei Y M 2005 Chaos Solitons Fract. 23 117
[10] Bi Q S 2005 Phys. Lett. A 344 361
[11] Li Z B, Zhang S Q 1997 Acta Math. Sci. 17 81 (in Chinese)[李志斌、 张善卿 1997 数学物理学报 17 81]
[12] Yan Z Y 2003 Chaos Solitons Fract. 18 299
[13] Wazwaz A M 2004 Appl. Math. Comput. 154 713
[14] Fan E G 2000 Phys. Lett. A 277 212
[15] Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese)[高 亮、 徐 伟、 唐亚宁、 申建伟 2007 物理学报 56 1860]
[16] Zhang L J, Chen L Q, Huo X W 2007 Nolinear Anal. 67 3276
[17] Yan Z Y 2002 Chaos Solitons Fract. 14 1151
[18] Zhu Y 2006 Nolinear Anal. 64 901
[19] Zhu Y 2005 Chaos Solitons Fract. 26 897
[20] Zhu Y 2007 Chaos Solitons Fract. 32 768
[21] Zhu Y 2006 Chaos Solitons Fract. 30 1238
[22] Guckenheimer J, Holmes P J 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer-Verlag)
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[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nolinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Wu Y Q 2010 Acta Phys. Sin. 59 1403 (in Chinese)[吴勇旗 2010 物理学报 59 1403]
[3] Huang W H 2009 Chin. Phys. B 18 3163
[4] Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 1476 (in Chinese)[曾 昕、 张鸿庆 2005 物理学报 54 1476]
[5] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、 张鸿庆 1998 物理学报 47 353]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、 杨红娟 2010 物理学报 59 67]
[7] Li J B, Zhan Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
[8] Guo B L, Liu Z R 2005 Chaos Solitons Fract. 23 1451
[9] Shen J W, Xu W, Lei Y M 2005 Chaos Solitons Fract. 23 117
[10] Bi Q S 2005 Phys. Lett. A 344 361
[11] Li Z B, Zhang S Q 1997 Acta Math. Sci. 17 81 (in Chinese)[李志斌、 张善卿 1997 数学物理学报 17 81]
[12] Yan Z Y 2003 Chaos Solitons Fract. 18 299
[13] Wazwaz A M 2004 Appl. Math. Comput. 154 713
[14] Fan E G 2000 Phys. Lett. A 277 212
[15] Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese)[高 亮、 徐 伟、 唐亚宁、 申建伟 2007 物理学报 56 1860]
[16] Zhang L J, Chen L Q, Huo X W 2007 Nolinear Anal. 67 3276
[17] Yan Z Y 2002 Chaos Solitons Fract. 14 1151
[18] Zhu Y 2006 Nolinear Anal. 64 901
[19] Zhu Y 2005 Chaos Solitons Fract. 26 897
[20] Zhu Y 2007 Chaos Solitons Fract. 32 768
[21] Zhu Y 2006 Chaos Solitons Fract. 30 1238
[22] Guckenheimer J, Holmes P J 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer-Verlag)
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